Degrees of freedom of TaaTP [Power / Sample Size]

posted by d_labes  – Berlin, Germany, 2019-05-14 14:01  – Posting: # 20282
Views: 1,693

(edited by d_labes on 2019-05-14 14:21)

Dear Helmut, dear Olivbood,

» ...
» » Furthermore, while the two parts of the trial will be evaluated as incomplete block designs, it seems to me that the original sequences and periods are preserved (e.g. an observation from period 3 is still coded as period 3), so that the degree of freedom would not be the same as for the conventional 2x2x2 crossover, no?
»
» Correct. Has some strange side-effects (see there).

To repeat the recommendation in this post:
The degrees of freedom are different for the 2x2 design and the design of the TaaTP.
We can mimic the df's, at least approximately, if we use the robust df's.

(TaaTP: Two-at-a-Time Principle)

But makes seldom a difference worth thinkin' about:
library(PowerTOST)
sampleN.TOST(CV=0.3, design="2x2x2", targetpower=0.9, print=FALSE)
  Design alpha  CV theta0 theta1 theta2 Sample size Achieved power Target power
1  2x2x2  0.05 0.3   0.95    0.8   1.25          52      0.9019652          0.9
sampleN.TOST(CV=0.3, design="3x6x3", targetpower=0.9, robust=TRUE, print=FALSE)
  Design alpha  CV theta0 theta1 theta2 Sample size Achieved power Target power
1  3x6x3  0.05 0.3   0.95    0.8   1.25          54      0.9112411          0.9

2 subjects more but due to balanced design, i.e. sample size has to be a multiple of 6.
If we go for an unbalanced design we have also a power of 90% with 52 subjects:
power.TOST(CV=0.3, design="3x6x3", robust=TRUE, n=52)
Unbalanced design. n(i)=9/9/9/9/8/8 assumed.
[1] 0.9005174

Regards,

Detlew

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